Multiplicativity of mapping degree
= Multiplicativity of mapping degree
{title2=$\deg(g\circ f)=\deg g\,\deg f$}
For maps of oriented connected <closed manifolds> of the same dimension, apply functoriality of <homology> to $f_*[M]=(\deg f)[N]$ and $g_*[N]=(\deg g)[L]$. The composite coefficient is their product. This recovers the multiplication of signed sheet counts for compositions of finite <covering maps>.